Numerical simulation of vertical-lateral competitive propagation of multiple fractures in multi-layered formations

Multi-cluster fracturing in vertically multi-layered formations faces critical challenges due to pronounced interlayer heterogeneity and uneven flow distribution among lateral fractures, resulting in unclear regulatory mechanisms of operational parameters on hydraulic fracture propagation. In this study, based on the equilibrium height growth model and the PKN-C model, the coupled solution of fracture length and height propagation is achieved through pressure iteration. By integrating the dynamic flow distribution mechanism of the resistance method, a simultaneous propagation model for multiple fractures in multi-layered formations is established. Furthermore, regulatory mechanisms of stimulation parameters on vertical-lateral competitive fracture propagation are systematically analyzed. The results demonstrate that interlayer mechanical contrasts induce non-smooth abrupt transitions in hydraulic fracture height profiles. The uniformity of multi-cluster fractures exhibits positive correlations with cluster number and spacing, while showing a negative correlation with injection rate. Additionally, cluster number and small cluster spacing (6-8 m) predominantly regulate vertical propagation, whereas injection rate and larger cluster spacing (≥10 m) exert stronger control over lateral propagation. The proposed workflow provides theoretical guidance for parameter optimization in multi-layered formations stimulation.